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How Distorted Food Prices Discourage a Healthy Diet

Roberto Pancrazi

University of Warwick

R.Pancrazi@warwick.ac.uk

Thijs van Rens

University of Warwick and Centre for Macroeconomics

J.M.van-Rens@warwick.ac.uk, tvanrens@gmail.com

Marija Vukotic

University of Warwick

M.Vukotic@warwick.ac.uk

February 2020∗

Abstract

We use data on purchase quantities and prices of healthy and unhealthy food to

show that diets are determined at least partially by the “food environment”. We

then estimate a structural model to argue that the effect of the environment is im-

portant: Distorted relative prices lead to underconsumption of fruit and vegetables

in the amount of around 15%, a third of the gap between the recommended and

actual intake. We show that it is possible to remedy these distortions with a policy

of taxes and subsidies that makes all consumers better off.

Keywords: food purchases, food prices, food consumption, retail access, supply ex-

ternalities, food deserts, nutritional inequality, healthy diet, obesity

JEL codes: D12, (E21,) H23, I12, I14, I18, L81

∗We thank Noriko Amano Patino, David Atkins, Diego Comin, Chris Edmond, Jessie Handbury, PaulHansen, Matthias Schundeln and Becca Taylor for helpful comments and suggestions. The empiricalresults in this paper are based on data from The Nielsen Company (US), LLC and marketing databasesprovided by the Kilts Center for Marketing Data Center at The University of Chicago Booth School ofBusiness. The conclusions drawn from the Nielsen data are those of the researchers and do not reflectthe views of Nielsen. Nielsen is not responsible for, had no role in, and was not involved in analyzingand preparing the results reported herein. We are grateful to the University of Warwick Global ResearchPriority in Food for funding the purchase of the Nielsen data.

1 Introduction

Diet-related disease leads to more preventable deaths in the US than any other risk

factor. Obesity and overweight by itself was the third-largest preventable cause of deaths

(11%) in 2005, after smoking (24%) and high blood pressure (20%). Including other

diet-related risk factors1 increases that contribution to 28% (Danaei, Ding, Mozaffarian,

Taylor, Rehm, Murray, and Ezzati (2009)). The situation in most other developed

economies is similar.2 This is a relatively new problem, with obesity rates increasing

sharply since 1980 (Ogden, Carroll, Curtin, McDowell, Tabak, and Flegal (2006)), which

is associated with staggering economic as well as human costs (Finkelstein, Trogdon,

Cohen, and Dietz (2009)). What determines our diets? And is there a role for policy to

improve what we eat?

A large literature in public health explores the effect of “obesogenic environments”

(Townshend and Lake (2017)), a term first coined by public health expert Boyd Swinburn

(Pincock (2011)). The environment may matter for obesity because of its effect on

inactivity (opportunities for exercise and active transport) or on diet, through access

to healthy food, advertising, labelling and food prices. We focus on the effect of prices,

which -as economists- we would consider likely to be the most important aspect of the

environmental determinants of diet, and which is also the area where the literature is

most lacking in convincing evidence (Cawley (2015)).3

It seems plausible that prices are least partly responsible for the deteriorating trend

in diet and therefore the obesity epidemic. Aggregate prices for healthy food groups,

in particular fruit and vegetables (Sturm (2005)), have increased relative to prices of

unhealthy food and drink (Wendt and Todd (2011)). The timing in these relative price

changes roughly lines up with the start of the obesity epidemic.4 However, there is a limit

to what we can learn from the time series, and it is almost impossible to disentangle

different possible explanations using aggregate data alone. In this paper, we study

variation in diet across households of different income levels in an attempt to better

understand the determinants of dietary choices, which will also help us to understand

the aggregate change in diets.

1High dietary salt (5%), low dietary omega-3 fatty acids found in seafood (4%), high dietary transfatty acids (4%), low intake of fruits and vegetables (3%), and low dietary poly-unsaturated fatty acids(1%). This excludes alcohol consumption, which is a sizeable risk factor for preventable death as well(3%).

2In the UK, for instance, the chief executive of NHS England warned that “Obesity is the newsmoking”, with obesity and overweight about to overtake smoking as the biggest cause of cancer (BBC(2014)).

3Cawley (2015) summarizes the problem as follows: “A large number of papers have regressed obesityor BMI on local food prices; the limitation of this approach is that variation in local food prices may bedue to differences in demand over geography and changes in demand over time and thus the estimatesof the impact of local food prices on weight may be biased.” (p.248) “Economic research with goodidentification strategies often is unable to reject the null hypothesis of no effect from many possiblecauses, such as food prices, ...” (p.261).

4The obesity epidemic in the US is generally considered to have started around 1980 (Ogden, Carroll,Curtin, McDowell, Tabak, and Flegal (2006)), although BMI among children started to increase at leasta decade earlier (Bell, Rogers, Dietz, Ogden, Schuler, and Popovic (2011)) and some studies have arguedits roots may date back as far as the early 20th century (Komlos and Brabec (2011)).

Our objective in this paper is to decompose the determinants of dietary choices

into preferences or demand shifters on the one hand, and the food environment or

supply shifters on the other. If diets are mostly determined by preferences, then the

role for government intervention may be limited. Therefore, we are most interested

in quantifying the role of distortions in the environment that generate inefficiencies in

dietary choices.

We start with a reduced-form analysis of purchase quantities and prices of food

from the Nielsen HomeScan data. We document that relative consumption of fruit and

vegetables, as a proxy for healthy food more generally, increases strongly with household

income as well as with average income in the county where households reside. This

dietary inequality is the variation that we aim to explain. We also show that relative

prices of fruit and vegetables increase with household income but decrease with average

county-level income for the poorer counties. These findings indicate that both demand

and supply factors are important for diets. If differences in diet were driven exclusively

by demand shifters, e.g. preference heterogeneity, then differences across households

would trace out the supply curve, and we would expect to see a positive correlation

between relative consumption and relative prices.

Our next step is to use a structural model to impose just enough structure on the

data to allow us to quantify the relative importance of demand and supply factors for

diets. The crucial element of the model is the retail technology for food. We assume that

there may be fixed costs associated with retailing food, which we think of as the costs

of the store and supply chain. The fixed costs generate a “backward-bending” supply

curve: the more food of a particular type is sold in a county, the cheaper it is, because

the fixed costs can be spread out over a larger amount of sales. This model predicts that

relative prices are inefficiently high for foods with large fixed costs of supply. We make

the model flexible enough to match the data by assuming that preference parameters

may vary exogenously with income. This allows for preferences to determine diets. We

then estimate the model so that the data inform us about the quantitative importance

of the various determinants of dietary inequality.

The identifying assumption we use to separate demand and supply factors is that

households that live and shop in the same location face the same prices. This assumption

allows us to use variation in prices and quantities across households within a county to

estimate heterogeneity in preferences and the relative demand elasticity. We then use

prices and quantities across counties to estimate the fixed costs of supplying food as the

remaining variation that is not explained by preferences. We implement the estimation

using non-linear simulated method of moments on the same data that we used for the

reduced-form analysis.

We find evidence for distortions in the relative price of healthy food, driven by a

large fixed costs in the supply of fruit and vegetables. Our estimates suggest that these

distortions result in a relative price that is about 40% higher and relative consumption

of fruit and vegetables that is about 15% lower than efficient. This effect of the food

environment on diets is smaller than the effect of preferences, but it is economically and

statistically significant and large. Moreover, there are many possible other externalities

that our not included in our model, and our estimates should therefore be interpreted

as a lower bound for the role of the food environment in discouraging a healthy diet.

Since dietary inequality due to price distortions in inefficient, there is a role for gov-

ernment intervention to improve diets. We show that, while any remedy for distortions

in food prices will generally affect the distribution across consumers, it is theoretically

possible to design an intervention that replicates relative prices as in the first-best allo-

cation and makes all consumers strictly better off. We then discuss a feasible tax and

subsidy policy that closely approximates this compensated Pareto-improving interven-

tion, and document its welfare gain and distributional effects.

Two recent papers in economics ask questions that are closely related to this study,

use the same data, but reach conclusions that are quite different and seem even directly

opposed to ours. Allcott, Diamond, Dube, Handbury, Rahkovsky, and Schnell (2019)

show that households of different income levels that buy food in the same store never-

theless make different choices over healthy and unhealthy food, illustrating the role of

preferences for diets. They also show that households that move to a healthier environ-

ment for exogenous reasons do not (immediately) change their diets very much, casting

doubt on the idea that there is an important role for the environment. Amano-Patino

(2020) estimates a demand system for food products on household panel data and sim-

ilarly finds that the role of prices in explaining differences in diet across households of

different income levels is very limited. We confirm the findings in these studies that the

effect of distortions in the food environment on dietary inequality is small. However, our

structural model estimates also allow us to show that these cross-sectional differences in

diet nevertheless indicate an important effect of distorted food prices on diets. In the

terminology of a randomized experiment: we use the (small) differences between poor

households (the treatment group) and rich households (the control group) to estimate

the effect of food prices on diets. These estimates then indicate that the effect of prices is

large, but affects both groups of consumers, with only small differences in the treatment

between treatment and control group.

The remainder of this paper is organized as follows. In section 2 below, we introduce

the Nielsen HomeScan data and document some patterns in dietary inequality that lead

us to conclude that healthy or unhealthy dietary choices are not determined exclusively

by preferences. To quantity the role of the food environment, we need to put some

structure on the data. Section 3 presents a simple and flexible structural model of con-

sumers’ choices between healthy and unhealthy food. We then discuss how we identify

and estimate this model in section 4. In section 5, we turn to our results. We show

that distorted relative food prices due to high fixed costs in the supply lead to inefficient

underconsumption of fruit and vegetables by 14 to 15.5%. Fixing this distortion would

close between a quarter and almost all of the gap between actual and recommended

intakes of fruit and vegetables. We also show that it is theoretically possible for the

government to intervene in such a way that makes consumers of all income levels and in

all locations strictly better off, and that such an intervention can be closely replicated

by a subsidy on fruit and vegetable consumption funded by an increase in progressive

income taxes.

2 Purchases of healthy and unhealthy food

We start this paper by documenting some patterns in food purchases by income. First,

we describe the data from the Nielsen HomeScan consumer panel, which we use to

measure food purchases. Then, we argue that one of the most striking differences in food

purchases between rich and poor that impacts a healthy diet is the underconsumption of

fruit and vegetables, which is much stronger for poor households. Finally, we document

that the comovement of quantities and prices of fruit and vegetables purchases in counties

of different income levels indicates that dietary inequality cannot be driven exclusively

by preferences or other demand factors.

2.1 Nielsen HomeScan Data

The HomeScan consumer panel, collected by Nielsen and distributed for academic use

by the Kilts Center for Marketing at Chicago Booth,5 is a dataset containing detailed

information about quantities and prices of food purchases by consumers. Participating

households are given a bar code scanner, and are instructed to scan their food purchases

at home and enter quantity purchased and expenditure for each item, so that unit prices

can be obtained simply by dividing expenditure by quantity. Basic demographic infor-

mation about the household is recorded as well. Importantly for this study, demographic

information includes household income and place of residence (ZIP code).

Purchase information is available for about 60, 000 households. Each household

records on average 172 shopping trips, and on each given trip records on average 7

product purchases with distinct Universal Product Code (UPC). The data are highly

disaggregated by product, because different varieties, different brands and different pack-

age sizes are all coded as different UPCs, resulting in 1.7 million distinct food products.

The complete dataset has around 50 million observations (product purchases) per year,

for ten years from 2004 to 2014.

A problem arises with random weight-items, foods that consumers purchase in any

quantity they desire and are charged for by weight or quantity. This problem affects

mostly fresh produce, but also unprepared meat, poultry and seafood; bread and baked

goods; deli counter items like cheese, deli meat, prepared salads and foods; bread and

baked goods; coffee; and dried vegetables and grains. In the dataset, these purchases are

recorded as “magnet data” with a generated UPC that is much more aggregated than

an actual UPC. In the first years of the sample, magnet data are only recorded as such.

5https://www.chicagobooth.edu/research/kilts/datasets/nielsen

From 2007, the “product group” of these magnet data is also recorded.6 Product groups

are 64 groups of similar UPC-level products, defined by Nielsen, which each constitute

up to 4.1% of the average household’s food expenditures. Examples of product groups,

ordered by expenditure share, are “bread and baked goods”, “snacks”, “packaged meats

- deli”, “fresh produce”, “cheese”, “prepared foods - frozen”, “milk”, “carbonated bever-

ages”, “candy” and “juice drinks - canned, bottled”. Since fresh produce is particularly

important for this study, we only use data for the 2007-2010 period, and we aggregate

products to the product group level.

We use a two-step procedure to aggregate product data to product groups as fol-

lows. First, we calculate household-level aggregate quantities for product groups as the

weighted sum of the quantities of all products in that group, using as weights the average

price of each product across households. Aggregating prices similarly is not possible,

because the household-specific prices are not observed for products that a particular

household does not purchase. Therefore, as the second step, we calculate household-

level aggregate prices for product groups by dividing household-level expenditures by

the household-level aggregate quantity. Apart from dealing with zero expenditures, this

procedure has the additional advantage that total expenditures are preserved with ag-

gregation. We normalize all aggregate prices to have an average of one across households,

so that all quantities are expressed as numbers of baskets of all products in a product

group.

Household income is provided in the Nielsen data. We add average income in the

location of residence for each household by matching their ZIP code to income data from

the Census,7 and then aggregating to the county level.8 Household income is coded as a

categorical variable, which we make continuous by assigning housholds an income level

corresponding to the midpoint of the income range represented by the income category

they are in. Household income then ranges from from $2500 to $120,000 per year in 16

categories.

2.2 Dietary inequality

We start by documenting how purchases of different types of food vary with income.

To document the relation between food purchases and income, we first project purchase

quantities and prices on a 10-th order polynomial in household and location income, and

then aggregate to 5%-tile bins in these variables. In some specifications, we also correct

for household composition and demographics, by including second-order polynomials

in household size, age and years of schooling (normalized at the sample mean), and

dummies for whether 2 adults are present in the household, and for household heads

6From 2010, the product group of magnet data is directly recorded in the data. Over the 2007-2010period, this information can be retrieved from the generated UPC for these purchases.

7https://www.psc.isr.umich.edu/dis/census/Features/tract2zip/8The number of ZIP codes is too large compared to the number of households in our dataset and

results in too few observations in each ZIP code to be able to document the relation between foodpurchases and income at this level. There are 3007 counties in the US, so that we have on average 20households in a county.

that are female, African American, Asian, other race, hispanic, part-time employed and

non-employed in the regression. Finally, we correct income (as well as food purchases)

for inflation and real income growth by normalizing the mean across households in each

year to equal the mean in 2010.

For each product group, we plot the quantity and the price at which foods in this

group were purchased against household and county-level income in 5%-tile bins. These

results are presented in appendix A. Assuming that food consumption closely tracks

food purchases, these graphs reflect differences in diet across households and locations

of different income levels. We analyze these dietary differences with a focus on what

may explain inequalities in health, particularly obesity.

One pattern in dietary inequality stands out, because it is both striking and likely

to affect health outcomes. Poorer households consume much less fresh produce than

richer households do. We argue that this difference reflects a broader difference in

the healthiness of the diet of poorer versus richer families. We show that the higher

underconsumption in poor households of fruit and vegetables does not depend on the

definition of fruit and vegetables. In figure 1, we show the consumption of fruit and

vegetables against household income, as a fraction of total food consumption. The diet

of the poorest 5% of households contains around 40% less fruit and vegetables than the

diet of the richest 5%. This difference is large compared to the overall underconsumption

of fruit and vegetables relative to the recommended intake of 40 − 60% above average

current intakes (U.S. Department of Health and Human Services and U.S. Department

of Agriculture (2020), Figures 2.3 and 2.4). We show that this finding is robust to four

different definitions of fruit and vegetables: (1) only fresh produce, as in the figure, (2)

also including frozen vegetables,9 (3) also including nuts, dried fruit, dried vegetables

and grains, and (4) also including canned vegetables, canned fruit, and pickles, olives

and relish.

9It is not possible to include frozen fruits, because these are coded in the same product group asdesserts.

Figure 1: Relative Consumption vs Individual Income

Note: This figure plots consumption of fruit and vegetables against household income, as a fraction

of total food consumption, against household income. Each point is a 5-percentile bin. The shaded

area represents a two standard-error confidence band.

Vegetables and fruits (and whole grains) are the most important two (three) of the

six components of a healthy eating pattern (U.S. Department of Health and Human

Services and U.S. Department of Agriculture (2020), chapter 1, p.15) and also the food

groups, for which current intakes are furthest below recommended levels. The aim of

this paper is to explore what causes this underconsumption. We will heavily rely on the

cross-sectional differences in fruit and vegetable consumption documented in figure 1 as

a source of identification, and as a by-product of our analysis, we will have some results

on the determinants of dietary inequality as well. We think of the share of fruit and

vegetables in a diet as a good summary measure of a healthy diet. We experimented

with various other definitions of healthy and unhealthy food, and always found very

similar patterns with income as for the relative consumption of fruit and vegetables.

2.3 Demand and supply determinants of healthy diets

What drives the difference in diet between poor and rich households? Clearly, there is

a role for demand factors. Innate preference over food differ across people, and these

preferences may be correlated with other characteristics and income. More generally,

“preferences” may be shaped by education, parental income and education, and social

economic status, all of which are correlated with income as well. There may also be

differences across consumers in the extent that they are aware of and care about the

health effects of their diet. On the other hand, it is equally clear that supply factors

may matter too. Much has been written about obesogenic environments, which may

feature limited access to healthy food, abundant advertising and marketing for unhealthy

food, and misleading food labels. One way, arguably the most important way, in which

the food environment affects dietary choices is through relative prices of healthy and

unhealthy food options. Recently, Allcott, Diamond, Dube, Handbury, Rahkovsky, and

Schnell (2019) make a powerful argument that preferences are an important determinant

of diets, and cast doubt on the relevance of the environment.

Comparing the prices paid for fruit and vegetables by income levels with quantities

purchased gives some insight into the relative importance of demand and supply factors.

These prices are shown in figure 2. Comparing relative prices of fruit and vegetables

in this figure to the relative quantities in figure 2 above seems to indicate that supply

factors are not very important: richer households not only consume a higher fraction of

their diet in the form of fruit and vegetables, but they also pay relative more for these

healthy foods. This suggest that their demand is higher, thus driving up the prices.

Figure 2: Relative Prices vs Individual Income

Note: This figure plots the relative price of fruit and vegetables against household income. Each point

is a 5-percentile bin. The shaded area represents a two standard-error confidence band.

But household-level purchase prices are not a good measure of market prices. There is

a wide variety of products within the “fruit and vegetables” category, and the household-

level price of the basket of fruit and vegetables will be determined in large part by

the household’s choice over which products from that basket to purchase. It seems

reasonable to expect that richer households will tend to buy higher-quality or more

desirable, more expensive types of fruit and vegetables, which may explain why these

households end up paying higher prices for this category of food.

A better measure of the food environment are the relative prices of healthy food in

a location. Figures 3a and 3b show the relative quantity of fruit and vegetables pur-

chased and the relative price of fruit and vegetables against income across counties. The

inequality in diet between poor and rich households carries over to inequality in diet

between poor and rich counties. The underconsumption of fruit and vegetables in the

poorest 5% of counties is about 25% larger than in the richest 5%, compared to a differ-

ence of 40% between the poorest and richest 5% of households. However, the differences

in income are also smaller across counties, and the gradient of underconsumption of fruit

and vegetables with income is actually higher across counties than across households.

Figure 3: Relative Consumption and Prices across locations

(a) Relative Consumption (b) Relative Prices

Note: The left panel plots the consumption of fruit and vegetables against income across counties, as

a fraction of total food consumption; the right panel plots the relative price of fruit and vegetables

against income across counties. The shaded areas represent a two standard-error confidence band.

Each point is a 5-percentile bin.

Although dietary inequality across counties looks similar or even stronger than across

households, the picture for relative prices now looks quite different. For the richest half

of counties, differences in diet still seem to be driven largely by differences in preferences,

as richer counties face less favorable relative prices of fruit and vegetables. However,

across poorer counties, the poorer the county, the higher the relative price of fruit and

vegetables. It is not possible to reconcile this negative correlation between relative

quantities and prices of healthy food with an standard upward-sloping supply curve

that is traced out by differences in demand factors.

We conclude that there must be a role for the environment in determining diets, at

least in poorer counties. Without further structure on the data, this is as far as we can

go. We now turn to a structural model that will allow us, with minimal assumptions,

to quantify the role of supply factors in determining diets.

3 A simple model of dietary choice

In this section we describe our model of dietary choice. This model is deliberately

simple. The aim is to impose just enough structure on the data to allow us to do welfare

analysis and counterfactuals decomposing dietary inequality across income levels into

a part that is driven by demand factors or preferences, broadly defined, and a part

that is determined by supply factors or the food environment. We therefore only model

consumers demand and retailers pricing decisions, and in both cases we allow for a large

part of the decisions that is not captured by the model through exogenous parameter

heterogeneity.

3.1 Consumers

Households, indexed by i ∈ N and living in location j ∈ K, differ from each other in

their income yij . The distributions of household income yij is exogenous. The model is

static and is assumed to hold in all time periods, so we suppress time subscripts.

Households spend an amount m (yij) of their income yij on food. Food expenditure

is exogenous, and will be chosen to match the data. They choose how to allocate their

total food expenditure between consumption of healthy food CH,ij and unhealthy food

CU,ij , in order to maximize their utility function over food.

u (CH,ij , CU,ij) =[α (yij) (CH,ij)

ε−1ε + (1− α (yij)) (CU,ij)

ε−1ε

] εε−1

The parameter α (yij) allows for preferences for healthy food to be correlated with income

yij . This non-homotheticity of the utility function is one way, by which preferences may

affect diets. The only real restriction on the variation of diets with income is that

the elasticity of substitution between healthy and unhealthy food ε is assumed to be

constant across households of different income levels.

Consumers maximize their utility u (CH,ij , CU,ij) subject to a standard budget con-

straint,

PH,ijCH,ij + PU,ijCU,ij = m (yij) (2)

where PH,ij and PU,ij are the prices of healthy and unhealthy food, which the household

takes as given. These prices may vary across households to reflect that different house-

holds live and shop in different locations j with potentially different price levels, but

also to allow for the possibility that richer households will buy food of higher quality.

This is the second way, by which preferences may affect diet.

The first-order conditions give the relative consumption of healthy over unhealthy

food as a function of preference parameters and prices.

CH,ijCU,ij

[1− α (yij)

α (yij)

PH,ijPU,ij

]−ε(3)

This is a (relative) demand equation, where ε is the price elasticity of demand. A

household consumes a healthier diet if their preference for healthy food α (yij) is stronger

or if healthy food is cheaper relative to unhealthy food.

3.2 Food retailers

Food, both healthy and unhealthy, is supplied by retailers. Retailers buy food from a

wholesaler, so that the marginal cost of healthy and unhealthy food of the same quality

is the same in all locations. However, the marginal costs differs with the quality of the

food. To the extent that some households purchase higher quality food than other, the

marginal cost of supplying this food will be higher too. We model this by assuming that

the marginal costs κH (yij) and κH (yij) vary exogenously with household income yij .

In addition to their marginal costs, retailers face a fixed cost of supplying healthy

food KH or unhealthy food KU in a particular location j, which may depend on the

location, so that KH (yj) and KU (yj) may vary exogenously with location income the

average income level of household in the location yj . This dependence reflects the fact

that it may be more expensive to run a store or operate a supply line in an area where

real estate is more expensive and traffic more congested.

We assume there is free entry of food stores in each location. The fixed costs generate

increasing returns to food supply, so that in equilibrium there will be a single store for

each food type in each location. However, the threat of entry implies that the local

monopoly is only sustainable if retailers make zero profits. This assumption is consistent

with the evidence in Altomonte, Barattieri, and Basu (2015), who show that firms price

as a markup over average rather than marginal costs.

A local sustainable monopoly with zero profits implies that prices are set just high

enough to recover fixed costs,

PH,ij =KH (yj)

CH,j+ κH (yij) (4)

PU,ij =KU (yj)

CU,j+ κU (yij) (5)

where CH,j =∑

i∈j CH,ij and CU,j =∑

i∈j CU,ij denote the total consumption in location

j of healthy and unhealthy food, respectively. Note that these pricing equations imply a

“backward bending” supply curve: the more food is sold, the lower the price the retailer

will charge for it.

Two observations are important for future reference. First, the fixed costs associated

with food supply introduce an externality: the more food of a certain type a household

purchases, the cheaper this type of food becomes for other households in the same

location that shop in the same store. This externality is the distortion in the food

environment that will generate inefficiencies in equilibrium diets. Second, although

prices are household-specific, only aggregate demand affects prices (by lowering the

impact of fixed costs on the average cost per unit sold). This property of the model will

be key to our identification strategy, see section 4.1 below.

3.3 Distortions in the food environment

The equilibrium of our model is defined as follows.

Definition 1 An equilibrium in our model is an allocation of quantities {CH,ij , CU,ij}and a set of prices {PH,ij , PU,ij}, ∀i ∈ N and j ∈ K, such that, for a given distribution

of income over households and locations, yij for all i ∈ N and j ∈ K:

(i) each household i maximizes its utility, so that equations (2) and (3) are satisfied

(ii) each retailer in any of the two sectors set prices satisfying (4) and (5) ∀i, k;

(iii) aggregation identities CH,j =∑

i∈j CH,ij and CU,j =∑

i∈j CU,ij are satisfied for

all locations j ∈ K.

Hence, the equilibrium is a well defined system of 4×N non-linear equations in 4×Nunknowns.

The equilibrium of our very simple model has some interesting properties. In this

paper, we largely ignore these and primarily use the model to quantity the sources of

dietary inequality. However, in order to build some intuition for the model, we briefly

describe some of its predictions here intuitively, with more detail provided in appendix

First, the model allows for a role of preferences as well as supply factors as drivers

of dietary inequality. Preferences broadly defined, generate differences in diet across

households of different income levels because of differences in the preference for healthy

food α (yij) or differences in the preference for quality κ (yij), which leads to differences in

prices. Inequality in diets that is driven by these two channels are efficient in the model,

and there is no role for government intervention.10 But the food environment matters as

well. Households that live in a location where there is low demand for healthy food will

face higher relative prices for healthy food, because the fixed costs have to be distributed

over a smaller base of aggregate sales of healthy food. Inequality in diets originating

from this effect is inefficient. The externality is a monopoly distortion, which creates

a coordination problem among consumers. If the government were able to coordinate

all households in a location to buy more healthy food, then these households would all

benefit from lower prices for healthy food.

The second model prediction we briefly highlight here, is that for sufficiently high

fixed costs the market for a particular type of food, e.g. healthy food, may completely

collapse. This happens when demand for healthy food is low, leading to high prices.

High relative prices of healthy food lead households to further substitute away from

healthy food, exacerbating the effect on prices. Eventually the price of healthy food

exceeds the monetized utility from the first unit of healthy food and in equilibrium no

healthy food is being demanded or supplied. Thus, the model predicts the emergence of

“food deserts” (Algert, Agrawal, and Lewis (2006), Powell, Slater, Mirtcheva, Bao, and

Chaloupka (2007), Larson, Story, and Nelson (2009), Sharkey, Horel, and Dean (2010)).

In this paper, we assume that markets for both types of food will remain open at all

times and do not exploit this interesting prediction, leaving it for future research.

10Of course, many possible externalities are missing from our simple model. For instance, if consumersdo not internalize the cost of health care for preventable disease caused by their diet, then this wouldjustify government intervention.

Third, the model gives an interpretation of the deteriorating trend in healthy diets

and the associated obesity epidemic. Distribution costs are an important component

of the cost of food (Kelsey (1989)) and technological progress in food “processing” has

dramatically reduced those costs (Schlosser (2013)). Unfortunately, processing makes

food unhealth, by removing spoilable nutrients (refining), adding chemical flavoring or

other additives and other processes like hydrogen-peroxide sterilization (Cutler, Glaeser,

and Shapiro (2003), Lustig (2012)). As a result, technological progress has been biased

toward unhealthy food, which may explain why relative prices of healthy food have risen

and relative consumption of healthy food has declined. Our model suggests that this

deterioration in diet as a result of technological progress may have reduced welfare.

4 Estimation results

We now proceed to estimate the model using the data described in section 2 and trying

to match the patterns in dietary inequality documented there. After discussing identifi-

cation, estimation and model fit, we briefly consider what we learn from the parameter

estimates. Then, in section 5, we use the estimated model for counterfactual analysis.

4.1 Identification

The objective of the estimation of the model is to find the demand shifters α (yij) and

supply shifters κH (yij) and κU (yij), which together describe the contribution of pref-

erences to differences in diet between households of different income levels, as well as

the fixed costs KH (yj) and KU (yj), which give rise to dietary inequality due to sup-

ply distortions, and other structural parameters like the demand elasticity ε, for which

the equilibrium allocation in our model -given the observed distribution of income over

households and counties in the data- replicates the observed patterns in food consump-

tion and prices as closely as possible. Estimating these parameters runs into the usual

identification problem in a simultaneous supply-demand system.

Our identifying assumption is that, whereas individual household demand depends

on household-specific prices, prices in the supply curve do not depend on individual

household demand, but only on aggregate consumption in the location, see equations

(4) and (5). This assumption allows us to solve the identification problem by using

variation in quantities and prices both across households within locations and across

locations.

Taking within-location deviations of the supply equations (4) and (5) gives PH,ij =

κH (yij) and PU,ij = κU (yij), where a hat over a variable denotes within-location devia-

tions, i.e. Xij = Xij−Xj . These equations immediately identify the income dependence

of the variable costs or preferences over quality. Moreover, since variation in prices across

households within locations is exogenous to household-level demand, we can identify the

relative demand equation in within-location deviations from an ordinary least squares

regression of the log of relative quantities of healthy over unhealthy food on the log of

relative prices and income.

(CH,ijCU,ij

)= −ε

(PH,ijPU,ij

)− ε

(1− α (yij)

α (yij)

This regression identifies the elasticity of substitution between healthy and unhealthy

food ε, as well as the income dependence of preferences for healthy food α (yij).

The intuition for our identification strategy is that households that live and therefore

shop in the same location face the same prices. Therefore any differences in the amount

of healthy and unhealthy food they purchase, and the prices they pay for these foods,

must be due to their preferences. This idea is very similar to the identification strategy

in Allcott, Diamond, Dube, Handbury, Rahkovsky, and Schnell (2019). However, we

extend their strategy in two ways. First, we disentangle preferences for healthy food

from preferences for quality. If we observe different households paying different prices,

we attribute that to differences in their preferences over quality. If we observe differences

in diet given the same prices, we attribute that to differences in preferences over healthy

versus unhealthy food. Second, having the structure provided by a structural model

allows us to go a step further: having identified the role of preferences from variation

within locations, we can then use the variation across locations to identify the role of

exogenous price shifters as well.

The supply and demand system described by equations (2), (3), (4) and (5) implies a

reduced-form relation of consumption of healthy food CH,ij , consumption of unhealthy

food CU,ij , and prices PH,ij and PU,ij of healthy and unhealth food, respectively, with in-

come. These relations depend on the income dependence of preferences α (yj), marginal

costs κH (yj) and κU (yj), and fixed costs KH (yj) and KU (yj). Since α (yj), κH (yj)

and κU (yj) follow directly from the within-location estimates of α (yij), κH (yij) and

κU (yij), the estimated reduced form allows us to identify the level and the income

dependence of the fixed costs, see appendix C for details.

4.2 Estimation and model fit

We implement the estimation of the model through non-linear simulated method of

moments. We find the model parameters that minimize the distance between model

and data for CH,ij , CU,ij , PH,ij and PU,ij for all levels of income. We summarize the

information in the data as the average value of these variables in 5%-tile bins for income,

both across households in deviation from the location average, and across locations.

This gives 160 moments to match (20 income quantiles for four variables, each both

within and across locations). To faciliate efficient estimation, we approximate the income

dependence of the parameters α (y), κH (y), κU (y), KH (y) and KU (y) as fourth-order

polynomials, which gives us a total of 26 parameters to estimate.

We weigh moments by the inverse of their variance, which we obtain directly from

the microdata. This solves the problem that different moments are in different units,

and also ensures the estimation is (approximately) efficient as in efficient GMM. Since

each moment is an average of a variable over a group of households in the microdata, the

variance of the moments is simply the variance of that variable divided by the number

of households in that group. Further details on the estimation procedure are given in

appendix D.

Figure 4 shows the model fit. The model is flexible enough to match almost perfectly

the variation of consumption of healthy food (fruit and vegetables), consumption of

unhealthy food (all other food) and their prices with income, both household income

in deviation from the county average, and county income. The only set of moments

that is matched less well is the steep increase of aggregate consumption of fruit and

vegetables with county income. The difference between the richest 5% of counties and

the poorest 5% is about 27 log points in the data, whereas in the estimated model this

difference is “only” 20 log points. The model could replicate this difference with the

income dependence of the preference for healthy food α (y). However, this parameter

also needs to match the gradient of fruit and vegetable consumption with income within a

county, which is slightly lower. Alternatively, the model could replicate the difference in

consumption of fruit and vegetables between rich and poor counties with a lower level or a

negative income dependence of the fixed costs of healthy food supply KH (y). However,

this would also affect the variation of the price of fruit and vegetables with county

income. The estimation procedure gives more weight to the variation in consumption

across households within counties than to its variation across counties, because the

former has tighther standard errors because of the much larger number of observations

in the underlying microdata. It gives more weight to variation in prices than variation in

consumption across counties, because prices have tighter standard errors because there

is less dispersion in prices than in consmption within counties.

Figure 4: Model and Data

Note: This figure displays the model fit. The left column plots consumption levels and the right

column plots price levels. The first row display consumption and prices of fruit and vegetable against

income in deviations from the county mean. The second row display consumption and prices of all

other food against income in deviations from the county mean. The third row display consumption

and prices of fruit and vegetable against county income. The forth row display consumption and

prices of all other food against county income. The purple dotted line plots the data moments with

the two standard error confidence bands displayed as the shaded area, while the blue solid line plots

the model moments. Each point is a 5-percentile bin.

The model fit is comfortably good enough that we can use the estimated model

for counterfactual analysis. The only set of moments, for which the estimated model

systematically and significantly differs from the data is still matched reasonably well.

Importantly, since differences in diet are due to differences within than across counties,

the relation of the relative consumption of fruit and vegetables with individual income,

as in figure 1, is matched almost perfectly, see figure 5.

Figure 5: Relative Consumption and Prices vs Individual Income

(a) Relative Consumption (b) Relative Prices

Note: The left panel plots the consumption of fruit and vegetables against household income,

as a fraction of total food consumption; the right panel plots the relative price of fruit and

vegetables against household income. The purple dotted line plots the data moments with

the two standard error confidence band displayed as the shaded area, while the blue solid line

plots the model moments. Each point is a 5-percentile bin.

4.3 Preference parameters

The estimates for the preference over food quality κH (y) and κU (y), and the preference

for healthy food α (y) are given in figure 6. These estimates are best understood by

considering their implications for consumption and prices.

Figure 6: Preference functions

(a) for Food quality

0 50 100 150

Individual Income (in 1000$)

(b) for Healthy food

0 50 100 150

nce function

Note: The left panel shows the estimated preference for food quality as a function of household income.

The solid blue line displays preferences for quality of healthy food, κH(y), and the dashed black line

displays preferences for quality of other food, κU (y). The right panel shows the preference for healthy

food in the utility function, α(y).

The estimated preference over healthy food quality corresponds almost one to one

to the price of fruit and vegetables in deviation from the county average, see the top

right-hand-side panel in figure 5. Richer households are willing to pay higher prices for

quality fruit and vegetables, and this relation is monotonic and approximately linear.

Households that are twice as rich as (100% richer than) the county average, pay on

average slightly over 2% more for an equal quantity of fruit and vegetables. The same

households pay on average around 1.5% more for other foods (see the second-row right-

hand-side panel in the figure), indicating that the estimated preference for quality over

unhealthy and healthy food is very similar.

The estimated preference for healthy food is determined primarily by the consump-

tion of fruit and vegetables in deviation from the county average, see the top left-

hand-side panel in figure 5. Household demand for fruit and vegetables is affected by

household-specific prices as well, but this effect is small.11 A household that is twice as

rich as the county average buys around 25% more fruit and vegetables than the county

average. This difference is much larger than the difference of around 10% in consumption

of other food. Preferences clearly have a role to play in explaining why richer households

have healthier diets than poorer families.

Relative prices and quantities are closely linked in our model through the elasticity

of substitution between healthy and unhealthy food ε, which is the elasticity of relative

demand for healthy food with respect to its relative price. We estimate ε = 0.44. This

value, which we identify from the comovement of relative prices and relative quantities

within counties, is in line with the literature on price elasticities of demand for food,

which reports elasticities for fruit between 0.41 and 0.98, and for vegetables between

0.44 and 0.71 (Andreyeva, Long, and Brownell (2010)).

4.4 Fixed costs and supply externalities

The estimated fixed costs in the supply of healthy and unhealthy food are shown in

figure 7. The first panel 7a shows the estimated values of the fixed costs and how they

vary with county income. Both fixed costs increase with average income in the county,

as we would expect because retail prices and congestion would tend to make running a

store in richer, more urban counties more costly.

The level of the fixed costs in healthy and unhealthy food cannot be easily compared,

because total expenditures on the two types of food (fruit and vegetables versus all other

food) are very different. Therefore, the second panel 7b in the figure plots the fixed costs

again, but as a share of the prices of healthy and unhealthy food, and against household

income rather than average income in a county. The main finding is that the fixed costs

for supplying fruit and vegetables is much higher than the fixed costs for supplying

other food. For fruit and vegetables, fixed costs account for 20 to 43% of the price,

whereas that same percentage is negligible (less than 1%) for other foods. The second

observation is that while fixed costs are higher in richer counties, they account for a

11For two reasons. First, the higher price of fruit and vegetables is partially offset by higher prices forother foods, due to a similar preference for quality over all foods. Second, given the estimated relativedemand elasticity, the effect of variation in relative prices on relative quantities is small compared tothe observed variation in relative quantities.

Figure 7: Fixed Costs

(a) Estimate

30 40 50 60 70 80 90 100

Average County Income (in 1000$)

(b) Share

0 50 100 150

FVOther food

Note: The left panel displays the estimated fixed cost as a function of county income. The solid blueline displays fixed cost in the healthy food sector, KH(y), and the dashed black line displays fixedcost in the other food sector, KU (y). The right panel displays the share of the price due to fixed cost,in percent, and is computed as (Kz (yj) /Cz,j) / Pz,ij , with z ∈ {H,U}.

larger share of prices for poorer households. This is because poorer households purchase

less food, and less fruit and vegetables in particular, which means that the fixed costs

need to be spread out over a larger amount of sales.

The finding that fixed costs are much higher for fruit and variables than for other

food is important, because it implies that the market for healthy food is much more

distorted than that for unhealthy food. Fruit and vegetable prices are in (large) part

the result of a monopoly distortion that drives up prices where demand is relatively low,

i.e. in poorer counties. The same is not true for other food, which is priced at very close

to marginal cost. This result is what will drive our counterfactual analysis in section 5

below.

Since the estimates of the fixed costs are crucial to our results, it is important to

understand exactly what identifies these estimates. The fixed costs are identified from

the variation in consumption and prices of healthy and unhealthy food across counties, in

particular from the U-shape in the relation of the (relative) price of fruit and vegetables

with average income in the county, see figure 3b. That means that they must help

the model to match both the negative income dependence of prices across counties at

low levels of income, and their positive income dependence at high income levels (over

and above the effect of preferences over quality, which explain some but not all of the

increase in prices with county-level income for richer counties).

The positive income dependence for richer counties is matched simply because fixed

costs increase with county income. The negative income dependence for poorer counties

is matched with the level of the fixed costs. The same level of fixed costs makes up a

larger share of the price in poorer counties, because demand is lower there, so that the

fixed cost needs to be distributed over a lower level of sales. This pushes up the relative

price of fruit in vegetables more in poorer counties. It is encouraging for our story that

it is possible to match the U-shape in fruit and vegetable prices across counties with

estimated fixed costs that are monotonically increasing in county-level income, even

though we do not impose this constraint (and that marginal costs are always estimated

to be positive, which we do not impose either).

5 Determinants of an unhealthy diet

We developed a structural model that we argue provides a plausible description of the

variation in consumption and prices of healthy and unhealthy food across households

and locations. We then estimated this model and showed that it fits the data well,

and that the parameter estimates seem reasonable and in line with previous estimates

insofar they can be compared. We now use this model for counterfactual analysis. In

particular, we ask the questions how much diet is affected by the type of distortions in

food prices that we consider in this paper, and what the government can do to fix these.

5.1 Distortions in food prices

We start by comparing the relative consumption of fruit and vegetables in equilibrium to

the first-best allocation. A social planner chooses the allocation of healthy and unhealthy

food for all consumers to maximize the weighted sum of their utility as in (1), using

Pareto weights θij to compare utility across consumers.

max{CH,ij ,CU,ij}i∈N

∑i∈N

θiju (CH,ij , CU,ij) (7)

Retailers make zero profits in equilibrium, so that we do not have to worry about

how profits are redistributed to consumers. The planner is constrained by the retail

technology, the distribution of consumers i ∈ N over locations j ∈ K, and the total

amount of food expenditure m (yij), and must respect the aggregate resource constraint.∑i∈N

[κH (yij)CH,ij + κU (yij)CU,ij ] +∑j∈K

[KH (yj) +KU (yj)] =∑i∈N

m (yij) (8)

In the efficient allocation, the relative consumption of healthy food depends only on

preference and marginal costs, which depend on preferences over quality.

CH,ijCU,ij

[1− α (yij)

α (yij)

κH (yij)

κU (yij)

]−ε(9)

Comparing the relative consumption in equilibrium (3) to the efficient allocation (9)

makes clear that equilibrium diets are distorted because prices do not reflect marginal

costs, given preferences for quality. Notice that the efficient relative consumption, and

therefore the distortions, do not depend on the Pareto weights.

The efficient allocation may also differ from the equilibrium in the distribution of

food over consumers: the social planner may want to redistribute food with respect

to the equilibrium consumption allocation. The efficient amount of redistribution will

depend crucially on the planner’s Pareto weights. For reasons of exposition, we will

start with the case of equal Pareto weights, θij = 1 for all i ∈ N , which will involve a

good amount of redistribution. However, we will focus on the case where Pareto weights

are chosen such that there is no redistribution at all. We do this in order to focus on the

distortions in relative food prices, in search of a government intervention that knows no

losers but only winners. The question what is the optimal amount of redistribution is

unrelated to the food environment and therefore outside the scope of this paper.

To find the efficient allocation without redistribution, we have to take a stance on

what “no redistribution” means. Clearly, the distributions of healthy and unhealthy food

over consumers will be different in the efficient allocation compared to the equilibrium,

and it is not straightforward to aggregate consumption of both types of food to total

food expenditures, because prices are not defined in the efficient allocation. We solve

for the no-redistribution efficient allocation by imposing two additional constraints on

the social planner’s problem. First, we assume that the planner does not move resources

across locations, so that the fixed costs of retailing healthy and unhealthy food in each

location must be paid for by consumers in that location. Second, we assume the planner

must fund the fixed costs by levying a proportional tax τ on equilibrium total food

expenditures mij . While the second constraint is clearly not implementable in practice

(we will consider implementability in section 5.3 below), it captures the assumption that

the planner does not want to change the distribution of total food consumption other

than shifting total food consumption up or down for all households.

The combined constraints on the planner’s problem can be represented by replacing

the aggregate resource constraint (8) by an resource constraint and a “planner budget

constraint” for each location j,∑i∈j

[κH (yij)CH,ij + κU (yij)CU,ij ] =∑i∈j

(1− τj)m (yij) (10)

KH (yj) +KU (yj) =∑i∈j

τjm (yij) (11)

where the planner chooses τj for all locations j in addition to the consumption allocation.

The constrained efficient allocation subject to these constraints, corresponds to the first-

best allocation with appropriate Pareto weights to prevent redistribution. The additional

constraints do not affect efficiency condition (9) for the relative consumption of healthy

and unhealthy food.

5.2 Effect of price distortions on diet

Figure 8 shows the relative consumption of fruit and vegetables in the first-best allo-

cation, as well as in the equilibrium allocation and in the data. For comparison, we

have also plotted the recommended intake of fruit and vegetables of at least 40% (U.S.

Department of Health and Human Services and U.S. Department of Agriculture (2020)).

Since the Pareto weights do not affect the relative consumption of healthy and unhealthy

food, the first-best allocation with equal Pareto weights is identical to the solution of

the planner problem without redistribution.

Figure 8: Relative Consumption - First best

30 40 50 60 70 80 90 100

Cons. F

ons. O

First Best

optimal diet

Note: This figure displays the relative consumption of fruit and vegetable, against county income, in

the data (purple dotted line), in the estimated model (solid blue line), and in the first-best efficient

allocation (dashed black line). The dashed red line represents the intake of fruit and vegetables

recommended by U.S. Department of Health and Human Services and U.S. Department of Agriculture

(2020). Each point is a 5-percentile bin.

Comparing the first-best to the equilibrium allocation, consumption of fruit and veg-

etables is 14 to 15.5% lower than efficient due to price distortions due to supply factors.

This effect is roughly constant for households of all income levels, and across counties

of different average income as well, and there is very little effect of price distortions on

dietary inequality. This explains why the difference-in-differences analysis in Allcott,

Diamond, Dube, Handbury, Rahkovsky, and Schnell (2019), which compared poorer to

richer households, reveals very little role for prices.

The effect of price distortions on diets is large. On average these distortions are

responsible for about one third of the gap between the actual and recommended intakes

of fruit and vegetables, ranging from almost a quarter for the poorest households to

almost the entire gap for the richest 5% of households, with the rest being due to

preferences. It is important to note that the role of supply factors we estimated is a

lower bound. The only inefficiency we consider is the effect of fixed costs in the supply

of healthy food. Other externalities that are likely to be important, most notably the

fact that consumers may not fully take into account the health effects on their diet,12

12This may be due to an ‘internality’, boundedly rational consumers discounting the long-term effectsof their dietary choices because of the difficulty of self-control (O’Donoghue and Rabin (2006), Haavioand Kotakorpi (2011)) or to moral hazard if consumers are insured for their health care costs.

are not included in our model and their effect will therefore be attributed to preferences.

In addition, preference are very broadly defined in our model and may themselves be

endogenous and possibly inefficient. This would be the case, for instance, if consumers

are uninformed (or ill-informed) about the health effect of their diet or influenced by

advertising or marketing by the food industry. In this paper, we deliberately focus on

a narrow set of supply factors, in order to make the case that even if we restrict the

analysis to price distortions, for which we find strong evidence from observable data,

there is a case for government intervention in the food environment. We will have nothing

to say about the effect of interventions such as information and education campaigns,

improved food labelling or restrictions in advertising, even though in reality these may

be important aspects of a government strategy to encourage healthy diets.

Figure 9: First Best

(a) Welfare

0 50 100 150

Average Welfare Gain: FB = 0.17

Average Welfare Gain: No Redr = 0.081

Average Welfare Gain: FB = 0.17

Average Welfare Gain: No Redr = 0.081

Equal weights (left)

No Redr. weights (right)

(b) Consump Other food

0 50 100 150

Equal weights

No Redr. weights

Note: The left panel plots welfare gains/losses against household income in the first-best allocation with respect

to the equilibrium, in percentage consumption-equivalent terms. The dotted black line (left y-axis) corresponds

to the first best allocation with equal Pareto weights, while the dashed green line (right y-axis) corresponds to the

first-best allocation with Pareto weights that imply no redistribution. The right panel displays the consumption

of other food in the these two first-best allocations together with the estimated level (solid blue line) and the

data (purple circled line). Each point is a 5-percentile bin.

Figure 9 show the difference between the first-best and the equilibrium allocation in

terms of consumers’ utility and consumption of “other food” (all food except for fruit

and vegetables). With equal Pareto weights, the planner redistributes consumption from

richer to poorer households, so that poorer households are much better off in the efficient

allocation (utility of the poorest 5% of households is higher in the first-best allocation by

a consumption equivalent of 20%), but richer households are made worse off, despite the

improvement in their diet. This picture is dramatically different when we choose Pareto

weights to avoid redistribution. In this case, presented in figure 9, richer households

are unambiguously better off in the first-best allocation, by a consumption equivalent

of slightly over 0.25%, because of their improved diet. However, poorer households

suffer a welfare loss from being taxed for the fixed costs of supplying healthy food that

they would not have chosen to consume in equilibrium. This is particularly true for poor

households living in rich counties, where the fixed costs of supplying fruit and vegetables

are higher.

5.3 An uncontroversial tax and subsidy policy

Which households are winners and which ones are losers from a policy that eliminates

price distortions due to fixed costs in the supply of fuit and vegetables depends on how

the planner funds this policy, in particular on how much consumption is redistributed

across households. This raises the question whether it is possible to design a policy

to eliminate distortions that makes all households better off. It is worth noting that

in the no-redistribution case, the average consumer in all counties is strictly better off

in the first-best allocation, as illustrated in figure 10, which plots welfare gains and

losses against county-level rather than household-level income. Within counties some

consumers are made worse off, because for them the utility loss from the higher tax on

consumption exceeds the utility gain from a better diet. We now explore whether it is

possible to compensate these losers through a different tax policy.

Figure 10: Welfare - Location Income

30 40 50 60 70 80 90 100

Welfare

Equal weights (left)

No Redr. weights(right)

Note: The left panel plots welfare gains/losses against county income in the first-best allocation with

respect to the equilibrium, in percentage consumption-equivalent terms. The dotted black line (left

y-axis) corresponds to the first-best allocation with equal Pareto weights, while the dashed green line

(right y-axis) corresponds to the first-best allocation with Pareto weights that imply no redistribution.

Consider a household-specific tax rate τij instead of a location-specific tax τj in

equations (10) and (11). We look for an income-dependent tax rate τij = τj (yij) that

generates the same welfare gain for all households within a county. Figure 11 shows that

this efficient allocation is indeed a compensated Pareto improvement over the equilibrium

allocation. The welfare gains from moving to the efficient allocation under this policy are

almost constant for all households at 0.1% of consumption. There are small differences

between households that live in different locations, but since we already showed that the

average household in each county improves its welfare, see figure 10, now that the welfare

gains are equalized within counties it must be that welfare improves for all households.

Figure 11: Pareto Improvement

(a) Welfare

0 50 100 150

Average Welfare Gain: Pareto Impr= 0.102

(b) Consump Other food

0 50 100 150

Pareto improv

Note: The left panel present welfare gains/losses against household income in the Pareto-improving

consumption allocation with respect to the equilibrium, in percentage consumption-equivalent terms.

The right panel displays the consumption of other food in the Pareto-improving allocation (orange

dashed diamond line) together with the estimated level (solid blue line) and the data (purple circled

line). Each point is a 5-percentile bin.

Under the Pareto-improving efficient allocation, fruit and vegetable purchases are

subsidized, and households are taxed for other food consumption at a rate that increases

with their income and varies with the location where they live, see figure 12. The

administration costs of this optimal policy would be very high, but it is possible to

approximate it with a simple rule that is feasible to implement in reality. This simple

rule would fund the subsidy on fruit and vegetables through the income tax, which

-different from a sales tax- allows to tax households progressively.

6 Conclusions

In this paper, we explore the question to what extent dietary choices are influenced by

the “environment” as opposed to preferences. This question is relevant, because if diets

are mostly determined by external factors, then there is a stronger case for government

intervention. We aim to establish a lower bound on the role of the environment, and

narrowly focus on distortions in the relative price for healthy versus unhealthy food.

Other possible distortions, for instance because consumers to not (fully) internalize the

health effects of their diet, are outside the scope of this paper.

We find that relative prices of healthy food are severely distorted, and fruit and

vegetables are 40% higher than is efficient. We also show that these price distortions

lead to inefficient underconsumption of fruit and vegetables by 15%, about a third

of the gap between actual and recommended intakes. In contrast, the effect of price

distortions on differences in diet across households of different income levels, is limited,

Figure 12: Tax Rates

(a) Individual Income

0 50 100 150

(b) Location Income

30 40 50 60 70 80 90 100

Note: This figure displays the implied tax rates τ in the Pareto-improving allocation as a function ofhousehold income, left panel, and county income, right panel.

which explains the contrast between our findings and those of recent previous studies.

While we use the same data, our approach differs from these previous studies in that

our results are based on estimates of a structural model of dietary choice, which allows

us to estimate aggregate effects and do welfare and counterfactual analysis.

Starting from the consumption allocation a benevolent social planner would choose,

we evaluate different policies to improve diets. We show that it is theoretically possible

to achieve efficient relative price levels without making any consumer worse off. We also

show that a simple tax and subsidy policy, which could be implemented in practice, gets

very close to replicating this first-best allocation, and we document its welfare gain and

distributional effects.

References

Algert, S. J., A. Agrawal, and D. S. Lewis (2006). Disparities in Access to Fresh

Produce in Low-Income Neighborhoods in Los Angeles. American Journal of Pre-

ventive Medicine 30 (5), 365–370.

Allcott, H., R. Diamond, J.-P. Dube, J. Handbury, I. Rahkovsky, and M. Schnell

(2019). Food Deserts and the Causes of Nutritional Inequality. The Quarterly

Journal of Economics 134 (4), 1793–1844.

Altomonte, C., A. Barattieri, and S. Basu (2015). Average-cost pricing: Some evidence

and implications. European Economic Review 79 (C), 281–296.

Amano-Patino, N. (2020). Nutritional Inequality: The Role of Prices, Income, and

Preferences. Cambridge Working Paper in Economics 1909, University of Cam-

bridge.

Andreyeva, T., M. W. Long, and K. D. Brownell (2010). The impact of food prices

on consumption: a systematic review of research on the price elasticity of demand

for food. American Journal of Public Health 100 (2), 216–222.

BBC (2014). Obesity is the new smoking, says NHS boss in England. BBC News:

Health, 18 September 2014.

Bell, J., V. Rogers, W. Dietz, C. Ogden, C. Schuler, and T. Popovic (2011). CDC

grand rounds: Childhood obesity in the United States. 60, 42–46.

Cawley, J. (2015). An economy of scales: A selective review of obesity’s economic

causes, consequences, and solutions. Journal of Health Economics 43 (C), 244–

Cutler, D. M., E. L. Glaeser, and J. M. Shapiro (2003). Why Have Americans Become

More Obese? Journal of Economic Perspectives 17 (3), 93–118.

Danaei, G., E. L. Ding, D. Mozaffarian, B. Taylor, J. Rehm, C. J. Murray, and M. Ez-

zati (2009). The preventable causes of death in the United States: comparative risk

assessment of dietary, lifestyle, and metabolic risk factors. PLoS Medicine 6 (4),

e1000058.

Finkelstein, E. A., J. G. Trogdon, J. W. Cohen, and W. Dietz (2009). Annual medi-

cal spending attributable to obesity: Payer-and service-specific estimates. Health

Affairs 28 (Supplement 1), w822–w831.

Haavio, M. and K. Kotakorpi (2011). The political economy of sin taxes. European

Economic Review 55 (4), 575–594.

Kelsey, R. (1989). Packaging in Today’s Society (3d ed.). Lancaster, PA: Technomic

Publishing Company.

Komlos, J. and M. Brabec (2011). The trend of BMI values of US adults by deciles,

birth cohorts 1882-1986 stratified by gender and ethnicity. Economics and human

biology 9, 234–50.

Larson, N., M. Story, and M. Nelson (2009). Neighborhood Environments: Dispar-

ities in Access to Healthy Foods in the U.S. American Journal of Preventive

Medicine 36 (1), 74–81.

Lustig, R. (2012). Fat Chance: Beating the Odds against Sugar, Processed Food,

Obesity, and Diseases. New York: Hudson Street Press.

O’Donoghue, T. and M. Rabin (2006). Optimal sin taxes. Journal of Public Eco-

nomics 90 (10-11), 1825–1849.

Ogden, C. L., M. D. Carroll, L. R. Curtin, M. A. McDowell, C. J. Tabak, and K. M.

Flegal (2006). Prevalence of overweight and obesity in the United States, 1999-

2004. JAMA 295 (13), 1549–1555.

Pincock, S. (2011). Boyd Swinburn: combating obesity at the community level. The

Lancet: Perspectives 378 (9793), 761.

Powell, L. M., S. Slater, D. Mirtcheva, Y. Bao, and F. J. Chaloupka (2007). Store

Availability and Neighborhood Characteristics in the United States. Preventive

Medicine 44, 189–195.

Schlosser, E. (2013). Fast Food Nation: The Dark Side of the All-American Meal.

New York: Perennial.

Sharkey, J. R., S. Horel, and W. R. Dean (2010). Neighborhood Deprivation, Vehicle

Ownership, and Potential Spatial Access to a Variety of Fruits and Vegetables in

a Large Rural Area in Texas. International Journal of Health Geographics 26 (9),

1–27.

Sturm, R. (2005). Childhood obesity - what we can learn from existing data on societal

trends, part 2. Preventing Chronic Disease 2 (2), A20.

Townshend, T. and A. Lake (2017). Obesogenic environments: current evidence of

the built and food environments. Perspectives in Public Health 137 (1), 38–44.

U.S. Department of Health and Human Services and U.S. Department of Agriculture

(2020). Guidelines for Americans 2015-2020 (8th ed.).

Wendt, M. and J. E. Todd (2011). The Effect of Food and Beverage Prices on Chil-

dren’s Weights. Economic Research Report 134705, United States Department of

Agriculture, Economic Research Service.

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